28. The distinction between solemn, sung and read Mass, sanctioned by the Instruction of 1958 (n. 3), is retained, according to the traditional liturgical laws at present in force. However, for the sung Mass (Missa cantata), different degrees of participation are put forward here for reasons of pastoral usefulness, so that it may become easier to make the celebration of Mass more beautiful by singing, according to the capabilities of each congregation.
These degrees are so arranged that the first may be used even by itself, but the second and third, wholly or partially, may never be used without the first. In this way the faithful will be continually led towards an ever greater participation in the singing.
29. The following belong to the first degree:
(a) In the entrance rites: the greeting of the priest together with the reply of the people; the prayer.
(b) In the Liturgy of the Word: the acclamations at the Gospel.
(c) In the Eucharistic Liturgy: the prayer over the offerings; the preface with its dialogue and the Sanctus; the final doxology of the Canon, the Lord's prayer with its introduction and embolism; the Pax Domini; the prayer after the Communion; the formulas of dismissal.
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36. There is no reason why some of the Proper or Ordinary should not be sung in said Masses. Moreover, some other song can also, on occasions, be sung at the beginning, at the Offertory, at the Communion and at the end of Mass. It is not sufficient, however, that these songs be merely "Eucharistic"—they must be in keeping with the parts of the Mass, with the feast, or with the liturgical season.
7. Between the solemn, fuller form of liturgical celebration, in which everything that demands singing is in fact sung, and the simplest form, in which singing is not used, there can be various degrees according to the greater or lesser place allotted to singing. However, in selecting the parts which are to be sung, one should start with those that are by their nature of greater importance, and especially those which are to be sung by the priest or by the ministers, with the people replying, or those which are to be sung by the priest and people together. The other parts may be gradually added according as they are proper to the people alone or to the choir alone.
8. Whenever, for a liturgical service which is to be celebrated in sung form, one can make a choice between various people, it is desirable that those who are known to be more proficient in singing be given preference; this is especially the case in more solemn liturgical celebrations and in those which either require more difficult singing, or are transmitted by radio or television.[6]
If, however, a choice of this kind cannot be made, and the priest or minister does not possess a voice suitable for the proper execution of the singing, he can render without singing one or more of the more difficult parts which concern him, reciting them in a loud and distinct voice. However, this must not be done merely for the convenience of the priest or minister.
Overall, it looks to me like the three-part structure prioritizes singing things that are short, easy, involve the congregation, and/or are repeated from week to week. This means unchanging dialogue and the Pater Noster in the first degree; in the next, the Ordinary. At the very end come the things that are long, complicated, changeable, and non-participational: the Gregorian Propers and the singing of the readings. The three-part framework can thus be seen to fail as a guideline for the music of the modern Mass.
Musicam Sacram is a dead letter, juridically speaking.
“The importance of the priest’s participation in the Liturgy, especially by singing, cannot be overemphasized. … ‘If, however. . . the priest or minister does not possess a voice suitable for the proper execution of the singing, he can render without singing one or more of the more difficult parts which concern him, reciting them in a loud and distinct voice. However, this must not be done merely for the convenience of the priest or minister.’ … Those priests who are capable should be trained in the practice of chanting the Gospel on more solemn occasions when a deacon may not be present. At the very least, all priests should be comfortable singing those parts of the Eucharistic Prayer that are assigned to them for which musical notation is provided in the Roman Missal. … If they are capable, deacons should be trained in the practice of chanting the Gospel on more solemn occasions.” (Sing to the Lord, USCCB, 19, 20, 21, 23, quoting Musicam Sacram 8)
I think it is not correct to say that MS is a dead letter simply because it predates some liturgical changes.
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